Solving Extended Linear Programming Problems Using a Class of Recurrent Neural Networks

Extended linear programming (ELP) is an extension of classic linear programming in which the decision vector varies within a set. In previous studies in the neural network community, such a set is often assumed to be a box set. In the paper, the ELP problem with a general polyhedral set is investigated, and three recurrent neural networks are proposed for solving the problem with different types of constraints classified by the presence of bound constraints and equality constraints. The neural networks are proved stable in the Lyapunov sense and globally convergent to the solution sets of corresponding ELP problems. Numerical simulations are provided to demonstrate the results.